I know that lots of people use towels in their cage. HOWEVER, in my experience a urine-soaked towel will begin to smell within a matter of minutes!:melodrama We only use towels for lap time, but never in the cage.
In order for this fleece setup idea to work at an optimal level, one must do certain things, most of which have been suggested. There is NO excuse for a room to smell like piggies unless the cage hygiene isn't good.
Here is my routine. The ONLY time my cavy cage has an odor is when we get close to the weekly change time. The "sniff test" is a great guide.lol
* If you can, vacuum the cage 3x/day.........or at a minimum, after the cavies have breakfast and before bedtime
* Have small pads to put under the most-soiled areas, and change those frequently
* Take the advice of those of us who have a lot of cavy experience. Why do you think we are so adamant about using uHaul pads? Because they work better than anything we've tried.
* Buy a spray called Clean Cage - it is NOT a cage cleaner, but a deodorizing agent. I spray the fleece pads and turn them over, spray the litter box before adding a light layer of litter, and even spray the cage liner and turn it over midweek. The spray won't hurt your piggies, but nevertheless, I avoid them having direct contact with it.
* Probably most important for you.........buy an air purifier. I will emphasize what a difference this makes. I have experimented with running the air purifier vs. not running it, and one can definitely smell the difference. I use the Homedics Air Purifier (smaller one) purchased from BBB with a 20% off coupon. It runs 24/7, is pretty quiet, and doesn't seem to draw much current.(broken link removed)
Take a look at your overall routine, change those things that need to be changed, and I promise you that you will be happy with the results.